JOSHUA JORTNER AND GABRIEL STEIN
2200
total effect will be a ratio of 1.013 to 1.020 for kl2/JCl3. Unfortunately, the carbon isotope effect
Vol. Gfi
does not help one decide whether the carbonmercury bonds are broken simultaneously or not.
DEUTERIUM ISOTOPE EFFECTS I N THE PHOTOCHERIICAL EVOLUTIOS OF HYDROGES FROM AQUEOUS FERROUS SQLUTIOKS BY JOSHUA JORTSER AND GABRIEL STEIN Department of Physical Chemastry, Hebrew University, Jerusalem, Israel Receavad May 8, 1068
The dependence of the isotope separation factor in the photochemical evolution of hydrogen from aqueous solutions of ferrous sulfate on the concentration of H +,ferrous, and ferric ions and on the concentration of an organic scavenger (methanol) was investigated. The results are interpreted in terms of a consecutive mechanism involving isotope separation in each of two steps. The respective separation factors in the first step (leading to H atom formation) and in the second (involving oxidation of Fez+by H) are derived. Isotope effects in radiation and photochemistry are compared. The isotope separation factors obtained support the intermediate hldiide formation mechanism for the oxidation of Fez+ hy 1% atoms.
Introduction The first investigation of the separation of hydrogen isotopes in the photochemical liberation of hydrogen from aqueous ionic solutions was carried out by Farkas and Farkas.‘ The purpose of their work mas the investigation of the isotope separation in a homogeneous system. In the irradiation of 0.05 M ferrous sulfate solutions in 0.05 N H2S04, isotope separation factors of 3.84.8 were obtained depending on the deuterium content of the so1utions.l The use of hydrogen isotope effects in photochemistry and radiation chemistry2 permits the study of primary photochemical radical formation processes by the technique of competitive reactions. In previous w 0 1 - k ~on ~ ~the photochemistry of the ferrous ion in aqueous solution, the mechanism of H atom formation and the oxidation mechanism by atomic hydrogen were investigated. In the present work we attempt to apply the isotope separation technique to obtain further information on the dissociation of the photoexcited ferrous ion in aqueous solution and the reactivity of €I atoms. Experimental Procedure.-Irradiations were carried out in fused silica vessels using 10 cc. of solution, and a low pressure Hg lamp operated a t 1000 v. and 100 ma. was employed as a light source. The light, was filtered by 0 5 cm. of 0.1 M NaCl solution, eliminating wave lengths below 2000 A. A t proximately 95y0 of the incident light Owas a t 2537 A. Irradiations were carried out at 20 f 1 The light intensity as determined by the uranyl oxalate actinometer was about 2 X 10-3 einstein l.-fmin.-l. Evacuation of the solutions was carried out as previously described.3 After irradiation the gas was transferred by a Toepler pump for isotope analysis. Materials and Solutions.-Deuterium oxide was purified by triple distillation from alkaline permanganate and KHSOI. Triple-distilled water and A.R. grade sulfuric acid and ferrous ammonium sulfate were used. Isotope Analysis.-The deuterium content of the liberated gas was determined by using the mass spectrograph built in this Department. The instrument was calibrated using hydrogen-deuterium mixtures prepared by decom-
.
(1) A. Farkas and L. Farkas, Trans. Faraday Soc., 3 4 , 1120 (1938). J. A p p l . Radiation Isotopes, 7 , 198 (1960). (3) J. Jortner and G. Stein, J . P h y s . Chem., 66, 1258 (1962). (4) J. Jortner a n d G. Stein, ibid., 66, 1264 (1962). ( 2 ) J. Jortner and G. Stein, I n t e r n .
position of standard solutions on Zn at 400”. The analysis was performed on mixtures of relatively low deuterium content so that HI and HD only need be considered. The isotopic composition was determined by the mass ratio 2.3 (H2:HD). Calibration and analysis were carried out a t the same gas pressure, which was in the region 10-6-2 X 10-6 mm. Tine experimental results were reproducible within f5%.
Results Ferrous Sulfate-H2S04 Solutions.-The experiments were carried out in solutions of relatively low deuterium content (D/H)l 0.2. We measured the isotope separation factor defined by N
(D,”)i X (E/D)g (1) where 1 and g refer to the liquid and tEe gas, and =
I> and H are in moles.
The dependence of the isotope separation factor on the irradiation time t (at constant light intensity) and sulfuric acid concentration was investigated. The results are presented in Table I . TABLE I ISOTOPE SCPARATIOX IU THE PHOTOCIIEMISTRY O R TIIL FERROUS Ion [HzSOIII,
N 0 78 78 78
70 .031 .0074 0065 0032 0009
-1
0 10 10 20 10 10
.10 10 10 10
+I, I.-’
103 i r r a
[re2+J0,
mole 1
t , min
mole
20 33 3G GO
10
47 60 130 140
150
I 10 1 10 0 35
s 4 0 4 0 3 0 4 2 4 0 4 1 4 0 3 8 3 7
These results indicate that within the experimental error the isotope separation factor is independent of the concentration of the ferric ion during irradiation. These results also indicate that the isotope separation factor is independent of the acid concentration in the region 0.8-0.01 N . In this region the rate of primary radical formation is pH d e ~ e n d e n t . ~ Isotope Separation in KF Solutions.-At low acid concentration (pH > 2) the accuracy of the isotopic analysis was reduced because of the low
Nov., 1962
PHOTOCHEMICAL EVOLUTION OF HYDROGEN FROM AQUEOUS FERROUS SOLUTIONS 2201
TABLE I11 gas yields obtained under irradiation. Therefore additional experiments were carried out in 0.1 ISOTOPE SEPARATION IN THE PHOTOCHEMISTRY OF Fe2 ION N KF solutions. The increa,se of the photoIN THE PRESENCE OF METHANOL chemical yield in the presence of the fluoride ion is [HzSO,] = 0.78N due to two factors. [Fe2+lor [ C H I O I ~ ] ~ , lOa[Fea+lt, (a) There is a reduction of the inner filter eft, mole mole mole 8 I.-' L-1 mm. fect3 of the ferric ion. The molar extinction COL-1 efficient of the ferric ion in 0.8 N H2S04 a t 2536 0.10 0 0.052 4.2 33 4 . 0 0.220 A. is reduced from E = 2800 to 600 1. mole-' .055 4.6 .254 52 1.05 .10 0.26 cm.--l by the addition of 0.1 M KF. The molar .050 5.0 50 0.75 .240 0.55 .10 absorption coefficient of the ferrous ion is un.047 5.1 51 .85 .240 .20 1.18 affected. 5.2 ,241 .047 47 .40 .10 1.25 (b) The ferric-fiuoride ion pair is stable to 5.5 .241 .045 49 .ll .05 1.22 reduction by H atom^,^ compared to the re.038 6.2 47 .04 .235 .025 1.20 activity of Fe3+0H- ion pairs present in sulfuric by determination with chromotropic acid. The acid solution a t high P H . ~ , ~ The experimental results presented in Table I1 decrease of the yield of Fe3+ with increasing indicate that the pH effect on the separation factor ratio [CH30H]/[F'e2+]is due to the competition is rather small. A slight decrease is observed at between reactions 1 and 2. Under conditions of high [CH80H]/[Fe2+]ratio (-50) the limiting high pH, within the range of experimental error. value of 6.2 f 0.3 was obtained for the isotope TABLE I1 separation factor. Under these conditions the yield of Fe3+ is only 1% of the yield obtained in ISOTOPE SEPARATION IN H2S04 SOLUTIONS CONTAININQ the absence of methanol. Hence H atoms react 0.1 A4 KF; [Fe2+Io= 0.1 M almost entirely by reaction 2, and the oxidation [HzSOn], N PH" s reaction (1) may be neglected. The very low value 4.2 0.78 of Fe3f obtained implies that the value of X is a .78 3.9 limiting one in view of the nearly total scavenging .09 2 8 39 of H atoms by methanol. .044 3.8 3.7 Q T h e pH was measured in identical solutions prepared Discussion from ordinary water. The contributions of the following steps to the isotope separation have to be considered: (a) The Effect of Methanol on Isotope Separation.In an attempt to determine the isotope separation primary radical formation; (b) interaction of H factor in the primary radical formation process, a and D atoms with the solvent; (c) oxidation of series of experiments was carried out in solutions ferrous ion by H and D atoms; and (d) reduction of containing ferrous sulfate, methanol, and 0.8 N the ferric ion by H and D atoms. The secondary process b probably does not consulfuric acid. In this system the atomic hydrogen tribute to the isotope separation in our case. The formed oxidizes ferrous i011~.~ exchange reactions with water and H+ ions are Fez+ H H + ---+ lyeS+ €I2 (1) relatively slow. Farkas and Farkas,I using kinetic data from gaseous phase experiments, claimed that or thc organic solu te6p7 for the exchange reaction of deuterium atom and water the activation energy is of the order of 16 CHpOH H +CII,OH 111 (2) kcal./mole. Friedman and Zeltman8 found for as in the radiation chemical investigation of this this reaction in aqueous solution a t pH 2 a ~ y s t e m . ~The . ~ radical CH20H thus formed may rate constant of 2 sec.-l. Radiation chemicalg' and photochemical4 evireact by dimerization and disproportionation dence indicates that the reduction of Fe3+ by H 2CHzOB --+ CEpO CHI013 (3) atoms is negligible a t low pH, the rate of reduction increasing with increasing pH. No isotope effect 2CHZOH + (CHZOH), was observed in this react,ion.fi Thus reaction d does not contribute to the isotope separations. 111 thc presence of the fcrric ion CII20H will act This conclusion is consistent with the independence as a reducing agcn t of the isotope separation factor of the irradiation CH2OH Fe3+ -+Fez+ CHzO H + ( 5 ) time and of the extent of photochemical oxidation. The separatiop factors presented in Tables I and At high [CH3OHl/[Fe2+] ratio the hydrogen atoms I1 include (a) the contribution of the primary €1 formed will react preferably in reaction 2 and the and D atom formation, and (c) a subsequent conferric ion formed will be reduced again according tribution rising from the oxidation reaction of the to reaction 5. Table I11 presents the experimental ferrous ion by H and D atoms. The experimental results. in the presence of methanol allow the The formation of formaldehylde was confirmed results separate determination of the two factors. ( 5 ) T.R i m , G. Stein, and J. Weiss, Proc. Roy. SOC.(London), b a l l , The rate of introduction into the bulk of the H +
(3 (3,
+ +
+
+
+
+
(a
+
+
+
375 (1952). (6) 3. H. Baxendale a n d G. Hughes, Z. physzk Chem. (Frankfurt;), 14,306 (1958). (7) J. H. Ba>.endale and G. Hughes, {bzd., 14,323 (1958).
(8) H. L. Friedman a n d A. H. Zeltman, J . Chem. Phys., 28, 878 (1958). (9) A. 0. Allen and W. G. Rothsohild, Radiation Res., 7,591 (1957).
JOSHUA JORTNER AKD GABRIEL STEIN
2202
and D atoms, produced from the excited state of the ion, will be represented schematically by the reactions kP4 __f
Fez+nq *--
_i+
+ Fe3+ H + Fea+ D
(PI
lipH and k,n represent the rate constants for radical
production a t constant light intensity. These quantities consist of the quantum yields for atom production (as defined in ref. 3 and 4) multiplied by the light intensity absorbed by the ferrous ion. These constants include a contribution for the preferential solvation of the light absorbing ferrous ion, and of th.e H + ion which acts as a scavenger4 transferring radicals into the bulk. The exchange of the atoms thus produced with the solvent is neglected, and only scavenging reactions have to be considered. The oxidation of the ferrous ion will be presented in the form
1coXH
H
+ Fe2+--
I ~
D
H,
+ Fe3+
koxD -+ HD
+ Fe3+
(1’)
kOXH
+ Fea+-
hOXD
-+ Dz
(2’)
As reaction 2’ leads in both cases to a rupture of a C-H bond. the isotoDe effect in this reaction is negligible. At high scavenger concentration and at low pH, second-order recombination of H and D atoms may be neglected. From this reaction scheme dlHr1 - kzECH30HI [HI dt ___-
IHD1 dt
+ l c o x a ( 1 - W )[€I][Fez-t-] +
1cz [CHsOH][D] -I- ~ ~ W O [HI W[Fez+]
~ O X H-( W ~ )[D][FeZ+l (11)
d’D’l dt where --E
(1 - WN”H ~ B [ C H ~ O H ]{ k o X H ( 1 - W ) d- kOxDW)[Fe2+]
+
[Dl
= WkpD
kz[CH30Hl
+ ( k o x ~ ( 1- W ) + ~ O X D WlFe2+] )
The experimentally determined quantity ie
(g)g
2[Hz1
+ [HDI
+
which a t low deuterium content of the solution is reduced to
In the integration of eq. I1 the contribution of the inner filter effect3 should be taken into account. However, as the right hand side of eq. IV’ is only dependent on the ratio of amounts of the hydrogen isotopes produced, the contribution of the inner filter effect cancels out. Using eq. 11,111,and IT7’,we obtain
+ lcz [CHaOH]
+ (1 - W )
(IT) Applying this equation to some limiting cases, the isotope separation factors in the primary radical production process, and in the oxidation reaction, can be obtained. Under limiting conditions when most of the radicals produced react with the organic scavenger, the separation factor observed is solely determined by the isotope separation in the primary process. This condition will be fulfilled when [CH30H]/[Fe2+] >> 1. Then we get
(g)g
=
1
+ (2 + k,JJ x
””)W
=
(1711)
and using the definition of W we readily get
(-) D H + D
(VI)
Defining thc separation factor X, in thc primary process for the introduction of H and D atoms into the bulk by
komW[D][Fe2+]
W
(Iv)
= ~ [ D z I [HDI
= 1.
iissuming that these rate constants are independent of the nature of the attacking atom, ~ O X Hand ~ Q X D represent the rate constants for the oxidation of the ferrous ion depending on whether H or D is detached. The atoms produced from the excited state of the ian may alternatively react with methanol
+ CHaOH +Hz + CHzOH D + CH3OH +H D + CHzOH
[HI =
(g)g
+ Feat
H
The steady state concentrations of the H and D radicals are presented by
(111)
kPH
---+
T‘ol. 66
1
Nov., 1062
PHOTOCHEMICAL EVOLUTION OF HYDROGEN FROM AQUEOUS FERROUS SOLUTIOES 2203
Application of the experimental results obtained under these limiting conditions (Table 111) leads to the value S, = 2.9 f 0.3. The isotope separation factor for the oxidation of ferrous ion by H and D atoms will be defined by sox =
kOXH
OX)
__
kOXD
This value can be obtained from the experimental results obtained for ferrous ion-H2S04 solutions in the absence of methanol when sufficient Fez+ is present for total scavenging of the atoms. Setting [CH,OH] = 0, the following expression is obtained for consecutive isotope separation at relatively low deuterium content
koxn
'
- W)
-+-
(10) F. Fiquet Fayard, J . chim. phys., 57, 467 (1960). (11) C. Lifshita, Ph.D. Thesis, Jerusalem, 1961.
I
6
(I;
5
JC,H
1 (X> I+ w 1 . 1 sox 8, Using the experimental results in the absence of methanol and the value of Sp previously obtained from eq. X we get Xox = 5 0 . 5 . The separation factors presented in Table I11 depend on the concentration ratio [CHBOH]/ [Fe2+fl. The gradual increase of the isotope separation factors with the increase of this ratio results from the competition between the scavenging reactions 1 and 2, The dependence of the isotope separation factors on the concentration ratio [CH30H]/[Fe2+] could be interpreted adequately by eq. 'c' using the values of S , and XOX previously obtained and setting li2/lCox~ = 0.15. The comparison between the calculated data and the experimental results is presented in Fig. 1. The rate constanhs ratio which was found to yield best agreement with the experimental results is in good agreement with the value of 01.17 obtained in ordinary water a t pH 16Jin acid solutions irradiated with ionizing radiations. In our previous ~ ~ on the r photochemistry k ~ ~ of Fez* ions it was shown that the mechanism of radical introduction into the bulk involves two distinct mechanisms: (a) a plH dependent process involving essentially electron sca\-enging by the H+aqion, and (b) a residual pH independent yield involving dissociative electron capture by a solvent molecule in the solvation layer of the excited ion. The H (or D) atom thus formed diffuses into the bulk. At pH 0.4, the contributioiis of these two reaction paths to the total quantum yield are about equaL3 In both these reactions roughly the same intramolecular isotope effect is expected.2 The primary photochemical isotope separation factor S,, obtained in the present work is identical within the experimentaI range of error witNhthe separation factor in the primary production of H and D atoms in the radiolysis of aqueous solutions, SA= 2.7 f 0.1 obtained a t low D content.lO.ll 2(1
I
7
4
I
0
20
I
40 [CH, OHl/[Fe2*l.
60
Fig. 1.-The dependence of the isotope separation factor in the presence of methanol on the concentration ratio [CHaOH][[Pe2f]. [H2S04] = 0.8 N ; (D/H)i = 0.22 to 0.25. Solid curve calculated from eq. V wlth ~ E + C H ~ O H / h + p e Z f = 0.15.
&,is equal to the separation factor in the radiation chemistry of aqueous solution^^^,^^ where H atoms are formed by the interaction of eaqwith H+aq. For the oxidation of Fez+ ion by H atoms, the separation factor SOX= 5 & 0.5 a t low deuterium content is obtained. Baxendale and Hughes7 derived a rate constants ratio of 2.4 between the rate constants for the oxidation of the ferrous ion in H20 and DzO. They considered this result as evidence against the oxidation mechanism involving the intermediate formation of the H2+molecule ion. The conclusions are not unambiguous,2 as an isotopic effect may be observed when the rates of an electron transfer reaction are compared in 820 and DzO. However, the marked isotope effect observed in the present work a t low D content definitely rules out the oxidation mechanism in~ volving H2+, since in the present case electron transfer in a medium of constant composition does occur. From the valueloof
a t low deuterium content, the isotope separation factor for the oxidation reaction can be derived, corrected for the preferential solvation of the hydroxonium ion. Denoting this corrected separation factor by X'OX we set X'ox = Sox/SEt. Using the experimental value SOX= 5 i 0.5 we get S'OX = 3, in fair agreement with the results of Baxendale and Hughes, Inveatigations of the oxidation of Fez+ by H atoms externally generatedf4 or produced ph~tochemically~.~ showed that this oxidation mechanism may involve the formation of a hydride intermediate14 (12) J. T. Allan and G. Scholes, Nature, 187, 218 (1960). (13) G. Czepski and A. 0. Allen, J . Phye. Chem., 66, 262 (1962). (14) G. Czapski, J. Jortner, and G. Stein, ibid., 68, 956, 960 (1961).
2204
Vol. 66
PAULDELAIXAY
+H
FeH2+,,
Fe’E32+aq+ H+aq
Fe3+aq
--+
(6)
d- HZ (7)
The isotope effect in the oxidation reactions is consistent with this reaction mechanism, as re-
action 7 involves the rupture of an 0-H bond in the hydroxonium ion. Achowledgment.-We thank Miss T. Feldman for valuable assistance. This work was sponsored by the Israel Atomic Energy Commission.
COULOSTATIC METHOD FOR THE KIKETIC STUDY OF FAST ELECTRODE PROCESSES. I. THEORY BY PAULDELAHAY Coates Chemical Laboratory, Louisiana State University, Baton Rouge, Louisiana Received M a y 3, 1068
A new method (charge-step or C O U Z Q S ~ U ~ ~ C ) for the kinetic study of fast electrode processes is discussed. The method involves: (a) charging of the electrode with a known quantitv of electricity by means of a coulostat to cause a departure from the equilibrium potential, and (b) recording of the overvoltage-time curve during the subsequent discharge of the double layer capacity cd by the electrode reaction. Overvoltage-time curves are derived for the following cases: constant cd and linearized current-overvoltage (I,) characteristic without mass transfer control or with mass transfer controlled by semi-infinite linear diffusion; constant cd and quadratic and cubic approximations of the I-q characteristic in the absence of mass transfer control; and variable double layer capacity. Conditions for pure control by either diffusion or the charge tranefer reaction are derived, and it is shown that conditions can be selected for which diffusion need not be considered when the apparent standard rate constant does not exceed 0 . 2 4 . 3 cm. set.-1. The method has about the same potentialities as the potentiostatic and single-pulse galvsnostatic methods but has the advantage of somewhat greater simplicity of technique and interpretation of results. The coulostatic method also allows the determination of the differential capacity of the double layer even when a fast charge transfer reaction occurs on the electrode.
A method, which is new to the writer’s knowledge, recently was suggested in this Laboratory for the study of fast adsorption processes at a metalelectrolyte interface’ and for electroanalytical determinations in the 10-5-10-7 34 concentration range.2 The method also can be applied to the kinetic study of fast electrode processes. The theory for the latter application is reported here, and experimental results are given in part II.3 The principle is as follows. The electrode being studied is initially a t equilibrium. The charge density on the electrode is changed abruptly (perhaps in 0.1-1 psec.) in such a may that the electrochemical cell is essentially a t open circuit once charging is completed (part I13). The potential departs from the equilibrium value as a result of the change of charge density. The increment of charge supplied to the electrode is consumed progressively by the electrode reaction, and the potential drifts back to its initial equilibrium value (unless there is a permanent change of the electrode). The overvoltage-time variations depend on the charge increment, the double layer capacity, and the characteristics of the electrode process. Study of electrode kinetics from oven-oltage-time curves thercfore should be possible. The expression “coulostatic method” was coined’ for this method when it is applied to adsorption kinetics because the charge density on the electrode remains constant during recording of potentialtime curves. Further, the instrument supplying a known charge might be called a “coulostat” by analogy with ((potentiostat.” The charge density varies in the study of electrode processes by this ( 1 ) P. Delahas and D. M. Mohllner, J. P h y s Chsn., 66, 959 (1962); J . A m C l e m . S o c , 84, Nov. 20 (1‘362). ( 2 ) P. Delahay, Anal. Cham. Acta, III pIesa. (3) P. Delahaj and A. Bramata, J. Phys. Chem., 66, 2208 (1962).
method since the double layer is discharged until the equilibrium potential is reached, and the expression ‘(charge-step method” might be preferable for application to electrode kinetics. However, there hardly seems a need for two expressions. The theory of the method will be developed for a simple charge transfer reaction, 0 ne = R, for which 0 and R are soluble. Processes without diffusion control will be considered first, and the effect of diffusion will be analyzed afterward. It will be assumed, as usual, that a large excess of supporting electrolyte is present.
+
Control by the Charge Transfer Reaction Overvoltage-Time Variations for the Linearized Current-Overvoltage Characteristic.-The increment of charge is Aq ==
qiii
- qi
(1)
wherc pi is the charge density a t the equilibrium ne = R potential for the electrode reaction 0 and qm is the charge density immediately after charging. It is assumed that the charging time is so short that leakage by the charge transfer reaction can be neglected during charging. The orervoltage ~ ( 1 7= E - E,, Eo equilibrium potential) a t time 1 after charging is
+
17 = ( 4
-
qi)/cd
(2)
where q is the charge density a t time t and Cd is the differential capacity of the electrode. It is assumed that variations of E are so small (1171 < 5 mv. approximately) that Cd is constant. The case of a variable double layer capacity is considered below. The signs in eq. 2 are cofisistent with the definition, q = E - E,, and the dependence of q on E , namely 17 2 0 for q - q, 0. The charge density q is
>
